Related papers: Can one classify finite Postnikov pieces?
Every $(\infty, n)$-category can be approximated by its tower of homotopy $(m, n)$-categories. In this paper, we prove that the successive stages of this tower are classified by k-invariants, analogously to the classical Postnikov tower for…
Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation…
We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.
We determine the Postnikov Tower and Postnikov Invariants of a Crossed Complex in a purely algebraic way. Using the fact that Crossed Complexes are homotopy types for filtered spaces, we use the above "algebraically defined" Postnikov Tower…
We give a functorial construction of k-invariants for ring spectra and use these to classify extensions in the Postnikov tower of a ring spectrum.
The first half of this paper is largely expository, wherein we present a systematic combinatorial approach to the theory of polynomial (semi)invariants and multilinear invariants of several vectors and covectors, for the classical groups.…
Although the Kadanoff-Baym equations are typically solved using time-stepping methods, iterative global-in-time solvers offer potential algorithmic advantages, particularly when combined with compressed representations of two-time objects.…
Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…
In this paper we outline a program for the classification of Floer-type theories, (or defining invariants of finite type for families). We consider Khovanov complexes as a local system on the space of knots introduced by V. Vassiliev and…
Vassiliev's knot invariants can be computed in different ways but many of them as Kontsevich integral are very difficult. We consider more visual diagram formulas of the type Polyak-Viro and give new diagram formula for the two basic…
We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…
We develop a theory of k-partitions of the set of infinite words recognizable by classes of finite automata. The theory enables to complete proofs of existing results about topological classifications of the (aperiodic) omega-regular…
We classify the completely integrable systems associated with classical root systems whose potential functions are meromorphic at an infinite point.
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
The classification of complex data usually requires the composition of processing steps. Here, a major challenge is the selection of optimal algorithms for preprocessing and classification (including parameterizations). Nowadays, parts of…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…